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- W2321849697 abstract "Let $( Ω , Α , mathbb{P} , tau )$ be an ergodic dynamical system.The rotated ergodic sums of a function $f$ on $Omega$ for $thetain mathbb{R}$ are $S_n^θ f : = sum_{k=0}^{n-1} e^{2pi i k theta} fcirc tau^k, n geq 1$. Using Carleson's theorem on Fourierseries, Peligrad and Wu proved in [14] that $(S_n^thetaf)_{n geq 1}$ satisfies the CLT for a.e. $theta$ when $(fcirctau^n)$ is a regular process. Our aim is to extend this result and give a simple proof based onthe Fejér-Lebesgue theorem. The results are expressed in theframework of processes generated by $K$-systems. We also considerthe invariance principle for modified rotated sums. In a lastsection, we extend the method to $mathbb{Z}^d$-dynamical systems." @default.
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- W2321849697 date "2013-01-01" @default.
- W2321849697 modified "2023-10-03" @default.
- W2321849697 title "The CLT for rotated ergodic sums and related processes" @default.
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- W2321849697 doi "https://doi.org/10.3934/dcds.2013.33.3981" @default.
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